At first glance, it looks like the Paris morgue in the 1790s after a hard day's guillotining: 50 poised princesses, who manage to stand upright and show off their aristocratic finery, despite just having lost their heads. The cadavers all have the same tall, slim body because they're all abstract replicas of a single person, the model who became a movie star and then swanned off to spend the rest of her life as a Serene Highness, arranging flowers in the Monaco palace and sending prissy reprimands to hotels and restaurants that allowed women to wear slacks.

The V&A's exhibition gives you scraps of Grace Kelly and fragments of Princess Grace. Along with the immobile parade of frocks – coolly understated in her Hollywood days, later more floridly matronly, then resplendently vulgar in the jewelled outfits she chose for charity balls – there are other relics detached from the body that wore them. One ghoulish case is full of horn-rimmed specs with no eyes to look through them, and dark glasses that can't protect the anonymity of someone who is invisible. Pairs of limp white gloves hang in the air, without the tell-tale smudges of grime they collected when the princess inspected sanitary conditions in the hospitals she visited. Saddest of all is her Hermès bag, so synonymous with her that the designers nicknamed it "the Kelly bag". It's obviously empty: how unlike the slim but ripely crammed Morris Louis case she carries in Hitchcock's Rear Window, from which she produces, to tantalise the stricken James Stewart, the flimsiest of nighties and a pair of slippers with peepholes for her curious big toes.

The exhibition's argument is that the transition from Hollywood to Monaco was easy and automatic: the Wasp patrician – who played a homegrown aristocrat in High Society, even though she lacked the horsey arrogance of Katharine Hepburn, her predecessor in the same role in The Philadelphia Story – acquired a throne and a diamond tiara to go with it. In fact Grace had traded down. The Oscar she won for The Country Girl, in which she achieved the theatrical miracle of making herself look drab and downtrodden, is a reminder that films require talent, not just the capacity to wave a permanently gloved right hand and to maintain a blandly gracious smile. Of course, royalty is an extension of the performing arts, but the show put on by Monaco resembled a tawdry Ruritanian operetta: Rainier got married in a costume based on the uniform worn by Napoleon's marshals, and despite his own lack of military credentials, loaded his chest with so many medals, orders and aiguilettes that he resembled a portly, mustachioed Christmas tree.

The transition between roles and continents, captured in a newsreel that flickers on the gallery wall, had its tricky moments. Grace arrived by ocean liner, and had to totter down a gangplank from a tender to meet Rainier, who was bobbing about expectantly on his yacht. Commuting between boats was complicated because she insisted on carrying her poodle, whose leash trailed dangerously around her feet; when Rainier grabbed it, he seemed to have tethered his fiancee. A figure in a fur coat, hardly appropriate wear for spring in the Mediterranean, dances anxious attendance: this must be Grace's mother, who had the woozy notion that Rainier was the Prince of Morocco and was presumably scanning the horizon for camels.

A portrait on the cover of the magazine Point du Vue shows Grace having sudden misgivings about the match. Inside a gilded border, she sits beside the smug Rainier, and as the shutter clicks she glances sideways with barely suppressed panic. The image – as the caption in the display case doesn't quite reveal – was a fake, but a revealing one. The portrait was actually taken for The Swan, in which Grace regretfully renounces her sexy tutor (Louis Jourdan) to marry an unalluring crown prince (Alec Guinness). The magazine simply put Rainier's head on the body of Guinness, without changing Grace's bereft expression. It's not the only diplomatic oversight in the exhibition's documentation: a dress designed for her by Oleg Cassini has a note beneath it saying that "They dated", which is a fairly demure way of describing their relationship. Even Grace's heavy-breathing biographer Donald Spoto manages to tell more of the truth when he confides that "their companionable affection advanced beyond its hitherto platonic phase".

Somehow the hats and the shoes, the gloves and the bags, the business-like suits and the spangled ballgowns don't add up into the woman, who was – at least until the protocol of the claustrophobic little principality stifled her – so dangerously larky and so frankly erotic. The hollow stiffness of the clothes looks foolish when you see Grace Kelly still alive on film, gliding seductively around the apartment in Rear Window or tipsily dancing with Frank Sinatra in High Society, or enjoying Cary Grant's terror as she drives him at reckless, exhilarated speed along a mountain road above Cannes in To Catch a Thief. She was indeed an icon, surrounded by adoring iconographers like Richard Avedon, who photographed her as a Greek statue in pink chiffon. But she owes her immortality to an iconoclast, a misogynistic director who did his best to damage her marble demeanour. It was Hitchcock who made her materialise in James Stewart's dozing brain like a wet dream in Rear Window, and had her offer herself to Cary Grant on a sofa in To Catch a Thief while a fireworks display outside the window fizzed in an iridescent orgasm; it was he who turned an attempt to strangle her in Dial M for Murder into a tortuous and brutally satisfying sex act. The V&A has the skins she shed, but the best way to see Grace Kelly is to close your eyes and remember how she showed James Stewart her negligee and, making a promise that she still keeps in our fantasies, murmured "Preview of coming attractions".